Two-dimensional transition rates improve life insurance reserve calculations.
problem Calculating life insurance reserves with Markov assumptions.
method Introducing two-dimensional forward and backward transition rates.
result Two-dimensional transition rates enable more accurate reserve calculations.
New definition for forward rates in multi-state models.
problem Defining forward rates in multi-state models.
method Established a theoretical framework and provided a novel definition.
result Interchanged transition probabilities and intensities in Kolmogorov forward equations.
A novel approach models rating transitions using Lie groups and Deep Learning.
problem Modeling rating transitions with geometric properties and stochastic processes.
method Introducing Itô-SDEs on Lie groups, using TimeGAN for calibration, and examining rating matrix properties.
result The geometric approach using Lie groups and Deep Learning generates a good fit for rating transitions.
A new model reduces rating transition matrix estimation errors for small portfolios.
problem Estimating rating transition matrices for small portfolios leads to unreliable and unstable predictions.
method A sparse structural model with three parameters that assumes an autoregressive mean-reverting ability-to-pay process.
result The model produces well-behaved transition probabilities, reducing statistical degrees of freedom and improving reliability.
Neural models learn continuous-time Markov chain transition rates from data.
problem Learning transition rates for complex stochastic systems.
method Neural networks to model nonlinear transition rates from observed data.
result Neural models outperform traditional methods in accuracy.
New method predicts default probabilities using rating transitions.
problem Estimating and predicting the probability of default in banking.
method Relates rating transition matrices to macroeconomic variables.
result Method provides more accurate estimates than Belkin et al. (1998).
Estimates transition rates of continuous-time Markov chains using imprecise probabilistic methods.
problem Estimating transition rate matrix from a finite-duration process.
method Imprecise probabilistic framework with conjugate priors and discrete-time analysis for hyperparameter determination.
result Continuous-time estimator with simple closed-form expression derived from discrete-time model.
We present a continuous-time maximum likelihood estimation methodology for credit rating transition probabilities, taking into account the presence of censored data. We perform rolling estimates of the transition matrices with exponential time weighting with varying horizons and discuss the underlying dynamics of trans…
The paper uses filtering techniques to predict rating transitions.
problem Analyzing the effect of business cycles on rating transitions.
method Point process filtering framework to infer latent factor states.
result Efficient estimation of latent factor parameters for real-time detection of economic changes.
The paper tackles robust control for insurance contracts under uncertain transition rates.
problem Maximizing utility in insurance contracts with uncertain transition rates.
method Novel robust utility maximization problem under bounded cumulative transition rate uncertainty, using worst-case scenario analysis.
result Existence and uniqueness of worst-case and best-case reserves for insurance contracts.
Researchers discover phase transitions in estimating object ranks from pairwise interactions.
problem Estimating the underlying ranks of objects from pairwise comparisons or collaborations.
method Characterized optimal statistical error rates for various signal-to-noise ratios.
result Phase transitions between optimal error rates of polynomial, exponential, zero, and trivial.
The paper uses machine learning and Lie groups to improve rating transitions and XVA calculations.
problem Improving rating transitions and XVA calculations using machine learning and Lie groups.
method Modeling rating transitions as SDEs on Lie groups, calibrating to historical and market data, applying Girsanov theorem, and using Deep Learning.
result Improves rating transitions and XVA calculations, making the model more robust.
The paper develops ML algorithms for calibrating credit rating transition models for high and low default portfolios.
problem Calibration of credit rating transition models for high and low default portfolios.
method Developed Maximum likelihood (ML) algorithms, including Laplace approximation for high-default portfolios and particle filter with Gaussian process regression for low-default portfolios.
result Both algorithms produce accurate approximations of the likelihood function and ML estimates of model parameters.
New CVs preserve transition rates in molecular dynamics.
problem Designing CVs that accurately capture rare events in high-dimensional systems.
method Integrating manifold learning and group-invariant featurization to construct neural network-based CVs that satisfy orthogonality conditions.
result Achieved a CV for butane that reproduces the anti-gauche transition rate with less than ten percent relative error.
New models for short rates show longer periods at higher rates.
problem Modeling longer periods of higher interest rates.
method Developed a class of time-homogeneous one-factor Markov diffusion models with specific boundary conditions.
result Explicit expressions for bond prices and transition densities in new probability measure.
ISOKANN learns collective variables and effective dynamics for metastable transitions.
problem Understanding metastable transitions in complex molecular systems.
method Integrates Koopman operators with neural networks to extract CVs and effective dynamics.
result Reconstructs coarse-grained kinetics and reproduces transition times across barriers.
New learning rate approach reveals phase transitions in SGD performance.
problem Understanding feature learning dynamics in neural networks.
method Characterizing the relationship between learning rate(s) and sample complexity for gradient-based algorithms.
result Phase transition from information exponent to generative exponent regime with different learning rates.
Study on bandit problems with switching constraints, revealing phase transitions in regret.
problem Stochastic multi-armed bandit problem with switching cost constraints.
method Proved matching upper and lower bounds on optimal regret, provided efficient algorithms.
result Phase transitions in optimal regret rate with respect to switching budget.
Catapult phase in neural nets shows exponential loss growth before quick decrease.
problem Understanding phase transitions in neural networks during training.
method Analyzing weight norm and loss behavior for super-critical learning rates.
result Proven existence of catapult phase in quadratic models and two-layer nets.
Method determines credit transition matrix from cumulative default probabilities.
problem Quantifying changes in bond credit ratings.
method Setup an ill-posed, linear inverse problem with entropy minimization.
result Method successfully determines CTM from cumulative default probabilities.
Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.
problem Approximating manifold heat semigroups from graph data under low regularity conditions.
method Iterating graph transition matrix P to approximate Qt=etΔ, bounding error in ∞-norm. result Convergence rates O(N−2/(d+6)) for manifold heat semigroup approximation, valid for in-sample and out-of-sample. We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heurist…
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high dimensional problems. In the {\it sparse regime} when the components are sufficientl…
There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are requir…
Two methods estimate rating transition probabilities, one Markov, one non-Markov, differing in default probabilities.
problem Estimating rating transition probabilities and default probabilities accurately.
method Markov and non-Markov frameworks, Fisher information matrix, self-exciting marked point processes.
result Non-Markov model yields higher default probabilities in investment grades, lower in speculative grades.
The paper models rating transitions and calibrates them to market data for XVA calculations.
problem Calibrating rating models to both historical and market data for accurate XVA calculations.
method Modeling rating transitions as a Markov chain, calibrating to historical and market data, proposing a novel calibration procedure.
result Improved XVA scheme through better calibration of rating models.
New rates and adaptive algorithm for nonparametric active learning under noise conditions.
problem Establishing new minimax-rates for active learning under noise conditions.
method Generic algorithmic strategy for adaptivity to unknown noise smoothness and margin.
result Achieves optimal rates in many general situations and avoids adaptive confidence sets.
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and ar…
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlo…
Elo rating outperforms complex models in skill estimation despite model misspecification.
problem Elo rating's reliability in skill estimation is questioned due to model misspecification.
method Interpreted Elo as online gradient descent and conducted synthetic experiments on non-BT models.
result Elo's superior performance in win rate prediction compared to complex models is explained through its sparsity and ranking effectiveness.
Model estimates LIBOR rates and finds COVID-19 spread spike due to credit risk.
problem Estimating LIBOR rates and understanding the factors affecting them.
method Developed a joint model for various LIBOR-related rates and used it to decompose spreads.
result Credit risk mainly caused the spike in LIBOR-OIS spread during the COVID-19 onset, with equal contributions from credit and funding-liquidity risks on average.
We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends…
We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and show that the validity of these assumptions - existence of a homogeneous genera…
Study measures investment funds' climate transition risk, finds moderate losses.
problem Measuring the impact of climate transition on investment portfolios.
method Comprehensive framework using geographical, sectoral, company and ISIN-level data.
result Investment funds suffer a moderate 5.7% loss in high transition risk scenario.
Paper details how to smoothly transition from EONIA to ESTR without significant financial impact.
problem Transition from EONIA to ESTR impacts financial instruments, especially OTC derivatives.
method Detailed analysis of how clean discounting approach based on ESTR affects pricing of OIS, IRS, and XVAs.
result The transition to EONIA-free pricing framework is safe and consistent, ensuring complete elimination of EONIA.
Study uniform rates for estimating Gaussian mixtures without separation assumption.
problem Estimating parameters in two-component Gaussian mixtures without separation.
method Uniform convergence rates derived using minimax lower bounds and careful analysis of polynomial equalities.
result Phase transition in optimal estimation rate based on mixture balance.
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
Unified error analysis for discrete flow models.
problem Error analysis of discrete flow models.
method Stochastic calculus theory, Girsanov theorem, generator matching, uniformization.
result First error analysis for discrete flow models.
The transition of several East and Central European countries and the countries of the Former Soviet Union from the socialist economic system to the capitalist one is studied. A recently developed microeconomic model for the personal income distribution and its evolution and a simple functional relationship between the…
New model explains deep learning performance at large learning rates.
problem Understanding deep learning performance at different learning rates.
method Developed neural networks with solvable training dynamics.
result Large learning rates lead to convergence to flatter minima.
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension d to scale with the series length T. We treat the transition matrix of time series as a nuisance parameter and directly apply sparse principal component…
New model for pairwise comparisons without stochastic transitivity.
problem Suboptimal performance of models assuming stochastic transitivity in real-world scenarios.
method Proposes a general family of statistical models using a skew-symmetric matrix.
result Achieves minimax-rate optimality and adapts to data sparsity.
Study examines USD exchange rate dynamics using Kramers-Moyal expansion.
problem Understanding and predicting exchange rate instability.
method Kramers-Moyal expansion and Fokker-Planck formalism applied to log-return data.
result Identifies a stabilizing linear drift and nonlinear diffusion term in exchange rate fluctuations.
New protocols show 1-bit mean estimation can be order-optimal without interaction.
problem Can 1-bit mean estimation be optimal without interaction?
method Adaptive and non-adaptive threshold and interval queries, with one adaptive transition.
result Arbitrary non-adaptive quantizers can match the adaptive rate, suggesting interaction is not necessary.
In an observed generalized semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition rate, to meet the existence of classical solution of the modified price equation, t…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal pro…
PCMC-Net uses neural networks to estimate transition rates in choice models, improving accuracy over traditional methods.
problem Inference limitations of traditional PCMC models when examples are scarce or new alternatives are observed.
method Amortized inference approach embedding PCMC definition into a neural network.
result Neural network outperforms feature engineered and machine learning models in airline booking prediction.